Spontaneous current generation in the 2SC phase

It is found that, except chromomagnetic instability, the gapless 2SC phase also exhibits a paramagnetic response to the perturbation of an external color neutral baryon current. The spontaneously generated baryon current driven by the mismatch is equivalent to the one-plane wave Larkin-Ovchinnikov-Fudde-Ferrell (LOFF) state. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo-Nambu-Goldstone current. We show this Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF state. We further point out that, when the charge neutrality condition is required, there exists a narrow unstable LOFF (Us-LOFF) window, where not only off-diagonal gluons but the diagonal 8th gluon cannot avoid the magnetic instability. We discuss that the diagonal magnetic instability in this Us-LOFF window cannot be cured by an off-diagonal gluon condensate in the color superconducting phase, and it will also show up in some constrained Abelian asymmetric superfluid/superconducting systems.